1. **State the problem:** Darin mows 90 lawns in 45 hours. We want to find how many hours it will take to mow 12 lawns at the same rate. 2. **Identify the formula:** Since the lawns are the same size and the rate is constant, the time taken is directly proportional to the number of lawns. We use the ratio: $$\frac{\text{Time}_1}{\text{Lawns}_1} = \frac{\text{Time}_2}{\text{Lawns}_2}$$ 3. **Plug in known values:** $$\frac{45}{90} = \frac{t}{12}$$ where $t$ is the unknown time for 12 lawns. 4. **Solve for $t$:** Multiply both sides by 12: $$t = 12 \times \frac{45}{90}$$ Simplify the fraction: $$t = 12 \times \frac{\cancel{45}}{\cancel{90}} = 12 \times \frac{1}{2}$$ 5. **Calculate the result:** $$t = 6$$ 6. **Interpretation:** It will take Darin 6 hours to mow 12 lawns at the same rate. 7. **Complete the table:** | Lawns | 90 | 12 | |-------|----|----| | Time (h) | 45 | 6 |